I have worked with MySQL more than MongoDB, but from what I've learned from MongoDB it's just what I needed, but it also has it's limitations that MySQL can do (for instance auto increment)
Would it be smart to use MongoDB for everything, and use MySQL for only certain things?
For instance use MongoDB to store users and everything else, but use MySQL to make for example a ticket system.
It sounds perfectly reasonable to use two database technologies in one project. Just make sure you use the right tool for the job.
It's common to use MySQL as the primary storage and MongoDB as caching/intermediate storage for speed.
You can for example have read-intensive data in MongoDB. The data for generating reports is perfect for a relational system like MySQL.